# Verification report

## Scope and provenance

This manuscript transfers the accepted complete-result research dossier
for AIM-ARITHMETIC_GEOMETRY-0078. Its original dated verification record
is preserved verbatim in `reproducibility/research_verification.json`.
The argument is computer-assisted; it has not received external human
peer review or formal proof-assistant verification.

The theorem is in characteristic zero and concerns the a=10 case.
Jelisiejew's published a=6,7,8,9 cases are combined only as a credited
corollary. The result gives a 104-dimensional reduced component support
and generic nonreducedness, not the length or multiplication of its
generic nilpotent local ring.

## Recorded mathematical checks

The dossier records the explicit 10-by-20 matrix over F_3, rank 35 for
S_1 W, five linear syzygies, 44 degree-five syzygies (24 minimal),
50 negative degree-one tangent directions, no tangents of degree at
most -2, and four translation directions. Direct syzygy lifts give a
490-dimensional second-order target, correction rank 40 and 244
independent obstruction quadrics on 46 normal coordinates.

Two exact msolve 0.10.1 F4 runs, with different degree-five batch
sizes, give leading powers of all 46 variables: squares for z1,...,z21,
cubes for z22,...,z35, fourth powers for z36,...,z45 and z46^5.
The independent parser verifies the recorded metadata, monomials,
single-term witness and file hashes. The equation system was regenerated
byte for byte during the research work; structural checks and the four
published cases were used as calibration. The characteristic-zero
implication is proved using projective properness, not inferred from
testing finitely many primes.

## Trust boundary and negative evidence

The two decisive runs use the same patched solver. The parser does not
independently prove membership of each reported polynomial in the
input ideal. The computation therefore depends on the correctness of
the solver and the narrowly documented patch. The companion archive
preserves that patch and the terminal transcript.

Degree four alone was insufficient because z46 was missing. The
supplementary Singular target run was terminated after over 90 minutes
with zero output and is not relied on. Collision-incidence estimates
and unfinished larger-prime or affine-chart computations are retained
as failed or partial routes, not proof certificates. There is no claim
of a full Groebner basis, a quotient-length computation, cross-engine
verification of the target, or a Lean proof.

## Package checks

The presentation and transfer checks record whether the displayed
matrix, the cited file hashes, copied computation artifacts and
minimal source archive agree with the accepted dossier. The final
manifest separately records actual compile diagnostics and inspected
page hashes. Packaging does not silently upgrade the mathematical
trust boundary or constitute an additional independent proof audit.

AI systems assisted the research, computation and manuscript preparation.
The author is responsible for the final text and later corrections.

The manuscript and this report are licensed under the Creative Commons
Attribution 4.0 International License (CC BY 4.0). The msolve-derived
patch is separately governed by the upstream software license.